What percent of the positive integers less than or equal to $100$ have no remainders when divided by $5?$
Solution: The only numbers that leave no remainder when divided by $5$ are those that are divisible by $5$. Starting from $1,$ every five integers is divisible by $5: 5,10,15,\ldots$ This continues even until the last group of five numbers $96$ through $100$ where $100$ is divisible by $5$. Therefore, since we have a whole number of groups of five and every group has exactly one element that is divisible by $5$, $1/5 = \boxed{20}$ percent of the integers less than $100$ have no remainders when divided by $5$.